I am 47 and my (adopted) daughter is 15. I know women in their 40s with newborn babies. Moms come in all ages, although it might be more common for moms of teens to be a bit younger. Women who have had careers, such as I did, tend to have children a little later in life, and moms of large families tend to be a little older.
Are we really "old?" When I was your age, I would have said that someone in their 40s was "old." Now that I'm this age, though, I understand what my great-grandmother said in her late 80s- that sometimes she still felt as though she should only be 12 years old again. She said that sometimes she couldn't believe how old she really was (and she grew up riding in a wagon pulled by mules, and lived to see the Space Shuttle.) Sometimes, even when you're a grownup, you look at yourself and wonder where all the years went. Sometimes it feels like you're still a kid or young person trapped in a body that is beginning to get arthritis and slow down a bit. Still, age DOES often bring wisdom. Older moms often have a lot of life-experience to share. Some are more patient and better able to help their kids than some younger moms, even if older moms may not be out playing soccer or climbing Mt. Everest.
Just love your mom for who she is. My own mother died when I was 8, and there have been many times in my life when I've wished she were still with us. Even if you sometimes get aggravated with your mom, cherish her and try to spend time with her.